Cremona's table of elliptic curves

129 = 3 · 43

Field	Data	Notes
Atkin-Lehner	3- 43+	Signs for the Atkin-Lehner involutions
Class	129b	Isogeny class
Conductor	129	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-92307627 = -1 · 33 · 434	Discriminant
Eigenvalues	1 3-  2  0  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,105,-191]	[a1,a2,a3,a4,a6]
j	129784785047/92307627	j-invariant
L	1.6091464597883	L(r)(E,1)/r!
Ω	1.0727643065255	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2064i4 8256j4 387d4 3225c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 129b4

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
1	-	2	0	0	-2	-6	4	-4	-6	8	6	2	+	4	-2	0	14	12	8	2	-8	0	14	-14

---

Quadratic twists for elliptic curve 129b4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	-43
2064i4	8256j4	387d4	3225c4	6321a4	15609j4	21801g3	37281b3	46569c3	68241i3	108489a3	123969a3	5547a4

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations